I posted this as an answer as suggested by Jorge Castro. I don't like duplicating information none too much, so I'm just pointing to the Super User post instead of copying all of it here...
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JonikMay 25 '11 at 15:06

When you say “make fonts look good”, you really mean “make fonts look like I'm used to” - if you were coming from a Mac you'd be asking “how do I prevent my fonts being distorted”.

Font rendering in Windows is heavily aligned to the pixel grid, trading sharp edges for distorted fonts. This corresponds to the “full hinting” option in Appearance→Fonts→Details. You shouldn't have to touch any further configuration.

Font rendering on OS X is the other way around - it does not distort the font shapes, meaning that most glyphs span a pixel boundary. This corresponds to the “none” hinting option.

By default, Ubuntu is somewhere in between - using slight hinting which distorts the fonts a bit to make them fit the pixel-grid better.

If you're using an LCD display you should have subpixel antialiasing enabled, regardless of the hinting type.

What I think really helped out my font smoothness was from adjusting the dpi.

First, open a terminal and type:

xdpyinfo | grep resolution

It'll give you a number like "96x96".

Now go to the Fonts tab in the Appearance settings. Click the details button in the bottom right corner.
At the top of this new window it has a place to put a number. Put the first number that terminal command gave you. For example, it gave me "108x106" so I put 108 there.

Doing this will get you closer to those smooth fonts you're looking for.

There are two main places where you can set the rendering of your fonts and at first sight they don't appear to have anything to do with each other:

gnome-appearance-properties shows you settings which apply to all GTK apps and allows you to choose various levels of smoothness and hinting. The settings here apply to all fonts equally. Other font settings such as the decision whether to hint or to autohint are taken from the following:

fonconfig is the program that is in charge of font configuration and font matching across the system. You make your choices by editing /etc/fonts/local.conf (~/.fonts.conf per-user) or by making symbolic links in /etc/fonts/conf.d to various presets in /etc/fonts/conf.avail. The technical details can be read by running man fonts.conf. Firefox and Chromium read their settings directly from here, only consulting gnome-appearance-properties if no hinting settings are found at all.

In my .fonts.conf I have four sections:

Whether each font is autohinted or hinted normally. To use autohinting explicitly, set hinting to true and autohinting to true. I have autohinting at slight for most fonts except for newer "expensive" fonts and MS fonts, which get hinted normally at medium. Exceptions are DejaVu Sans Condensed, Lucida Grande, PT Sans, Segoe and Tahoma which are hinted slightly. I think the Windows style is normal hinting at full/medium (which are typically the same). The freetype documentation says that autohinting will be applied if no truetype hinting information is supplied with the font and that seems to apply in Firefox too. Take care that the .fonts.conf doesn't conflict with the presets.

The substitutions and fallbacks that apply if a font is not found on the system. I swap DejaVu Sans Condensed for Tahoma, DejaVu Sans for Geneva, Arimo for Arial, Mukti Narrow for Lucida Grande and FreeSans for Helvetica.

Once you have written your .fonts.conf open Wikipedia and by choosing your default proportional font to be sans-serif in Preference>Content>Advanced you can quickly see how each font looks by using the arrow keys on the Default Font as shown in the picture.

Alternatively, Igor's blog has a test page where you can compare all the different rendering options side by side for a particular font.

Your first stop is the GNOME’s configuration settings for fonts, located in System->Preferences->Appearance under the Fonts tab. If you’re using an LCD display make sure you have the subpixel smoothing rendering mode enabled. Click Details to get access to the hinting options. Play around with these to get a result you like.

Here’s a sample of my system’s fonts configured with these settings:

There are many more options for font rendering available with a .fonts.conf file. This file, from this forum post, turns on a hinting feature that is usually disabled due to patent issues with Apple.

Copy and paste the text above into a text file, and save it in your home directory as .fonts.conf (note the first period, this file will be hidden). Log out for the changes to take effect. Here’s a sample of fonts with this file: